1/* Copyright (C) 2004-2022 Free Software Foundation, Inc.
2 This file is part of the GNU C Library.
3
4 The GNU C Library is free software; you can redistribute it and/or
5 modify it under the terms of the GNU Lesser General Public
6 License as published by the Free Software Foundation; either
7 version 2.1 of the License, or (at your option) any later version.
8
9 The GNU C Library is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
12 Lesser General Public License for more details.
13
14 You should have received a copy of the GNU Lesser General Public
15 License along with the GNU C Library. If not, see
16 <https://www.gnu.org/licenses/>. */
17
18#include "div_libc.h"
19
20
21/* 64-bit signed long remainder. These are not normal C functions. Argument
22 registers are t10 and t11, the result goes in t12. Only t12 and AT may
23 be clobbered.
24
25 Theory of operation here is that we can use the FPU divider for virtually
26 all operands that we see: all dividend values between -2**53 and 2**53-1
27 can be computed directly. Note that divisor values need not be checked
28 against that range because the rounded fp value will be close enough such
29 that the quotient is < 1, which will properly be truncated to zero when we
30 convert back to integer.
31
32 When the dividend is outside the range for which we can compute exact
33 results, we use the fp quotent as an estimate from which we begin refining
34 an exact integral value. This reduces the number of iterations in the
35 shift-and-subtract loop significantly.
36
37 The FPCR save/restore is due to the fact that the EV6 _will_ set FPCR_INE
38 for cvttq/c even without /sui being set. It will not, however, properly
39 raise the exception, so we don't have to worry about FPCR_INED being clear
40 and so dying by SIGFPE. */
41
42 .text
43 .align 4
44 .globl __remq
45 .type __remq, @funcnoplt
46 .usepv __remq, no
47
48 cfi_startproc
49 cfi_return_column (RA)
50__remq:
51 lda sp, -FRAME(sp)
52 cfi_def_cfa_offset (FRAME)
53 CALL_MCOUNT
54
55 /* Get the fp divide insn issued as quickly as possible. After
56 that's done, we have at least 22 cycles until its results are
57 ready -- all the time in the world to figure out how we're
58 going to use the results. */
59 stt $f0, 0(sp)
60 excb
61 beq Y, DIVBYZERO
62
63 stt $f1, 8(sp)
64 stt $f3, 48(sp)
65 cfi_rel_offset ($f0, 0)
66 cfi_rel_offset ($f1, 8)
67 cfi_rel_offset ($f3, 48)
68 mf_fpcr $f3
69
70 _ITOFT2 X, $f0, 16, Y, $f1, 24
71 cvtqt $f0, $f0
72 cvtqt $f1, $f1
73 divt/c $f0, $f1, $f0
74
75 /* Check to see if X fit in the double as an exact value. */
76 sll X, (64-53), AT
77 ldt $f1, 8(sp)
78 sra AT, (64-53), AT
79 cmpeq X, AT, AT
80 beq AT, $x_big
81
82 /* If we get here, we're expecting exact results from the division.
83 Do nothing else besides convert, compute remainder, clean up. */
84 cvttq/c $f0, $f0
85 excb
86 mt_fpcr $f3
87 _FTOIT $f0, AT, 16
88 mulq AT, Y, AT
89 ldt $f0, 0(sp)
90 ldt $f3, 48(sp)
91 cfi_restore ($f1)
92 cfi_remember_state
93 cfi_restore ($f0)
94 cfi_restore ($f3)
95 cfi_def_cfa_offset (0)
96 lda sp, FRAME(sp)
97 subq X, AT, RV
98 ret $31, (RA), 1
99
100 .align 4
101 cfi_restore_state
102$x_big:
103 /* If we get here, X is large enough that we don't expect exact
104 results, and neither X nor Y got mis-translated for the fp
105 division. Our task is to take the fp result, figure out how
106 far it's off from the correct result and compute a fixup. */
107 stq t0, 16(sp)
108 stq t1, 24(sp)
109 stq t2, 32(sp)
110 stq t5, 40(sp)
111 cfi_rel_offset (t0, 16)
112 cfi_rel_offset (t1, 24)
113 cfi_rel_offset (t2, 32)
114 cfi_rel_offset (t5, 40)
115
116#define Q t0 /* quotient */
117#define R RV /* remainder */
118#define SY t1 /* scaled Y */
119#define S t2 /* scalar */
120#define QY t3 /* Q*Y */
121
122 /* The fixup code below can only handle unsigned values. */
123 or X, Y, AT
124 mov $31, t5
125 blt AT, $fix_sign_in
126$fix_sign_in_ret1:
127 cvttq/c $f0, $f0
128
129 _FTOIT $f0, Q, 8
130 .align 3
131$fix_sign_in_ret2:
132 ldt $f0, 0(sp)
133 stq t3, 0(sp)
134 cfi_restore ($f0)
135 cfi_rel_offset (t3, 0)
136
137 mulq Q, Y, QY
138 excb
139 stq t4, 8(sp)
140 mt_fpcr $f3
141 cfi_rel_offset (t4, 8)
142
143 subq QY, X, R
144 mov Y, SY
145 mov 1, S
146 bgt R, $q_high
147
148$q_high_ret:
149 subq X, QY, R
150 mov Y, SY
151 mov 1, S
152 bgt R, $q_low
153
154$q_low_ret:
155 ldq t0, 16(sp)
156 ldq t1, 24(sp)
157 ldq t2, 32(sp)
158 bne t5, $fix_sign_out
159
160$fix_sign_out_ret:
161 ldq t3, 0(sp)
162 ldq t4, 8(sp)
163 ldq t5, 40(sp)
164 ldt $f3, 48(sp)
165 lda sp, FRAME(sp)
166 cfi_remember_state
167 cfi_restore (t0)
168 cfi_restore (t1)
169 cfi_restore (t2)
170 cfi_restore (t3)
171 cfi_restore (t4)
172 cfi_restore (t5)
173 cfi_restore ($f3)
174 cfi_def_cfa_offset (0)
175 ret $31, (RA), 1
176
177 .align 4
178 cfi_restore_state
179 /* The quotient that we computed was too large. We need to reduce
180 it by S such that Y*S >= R. Obviously the closer we get to the
181 correct value the better, but overshooting high is ok, as we'll
182 fix that up later. */
1830:
184 addq SY, SY, SY
185 addq S, S, S
186$q_high:
187 cmpult SY, R, AT
188 bne AT, 0b
189
190 subq Q, S, Q
191 unop
192 subq QY, SY, QY
193 br $q_high_ret
194
195 .align 4
196 /* The quotient that we computed was too small. Divide Y by the
197 current remainder (R) and add that to the existing quotient (Q).
198 The expectation, of course, is that R is much smaller than X. */
199 /* Begin with a shift-up loop. Compute S such that Y*S >= R. We
200 already have a copy of Y in SY and the value 1 in S. */
2010:
202 addq SY, SY, SY
203 addq S, S, S
204$q_low:
205 cmpult SY, R, AT
206 bne AT, 0b
207
208 /* Shift-down and subtract loop. Each iteration compares our scaled
209 Y (SY) with the remainder (R); if SY <= R then X is divisible by
210 Y's scalar (S) so add it to the quotient (Q). */
2112: addq Q, S, t3
212 srl S, 1, S
213 cmpule SY, R, AT
214 subq R, SY, t4
215
216 cmovne AT, t3, Q
217 cmovne AT, t4, R
218 srl SY, 1, SY
219 bne S, 2b
220
221 br $q_low_ret
222
223 .align 4
224$fix_sign_in:
225 /* If we got here, then X|Y is negative. Need to adjust everything
226 such that we're doing unsigned division in the fixup loop. */
227 /* T5 records the changes we had to make:
228 bit 0: set if X was negated. Note that the sign of the
229 remainder follows the sign of the divisor.
230 bit 2: set if Y was negated.
231 */
232 xor X, Y, t1
233 cmplt X, 0, t5
234 negq X, t0
235 cmovne t5, t0, X
236
237 cmplt Y, 0, AT
238 negq Y, t0
239 s4addq AT, t5, t5
240 cmovne AT, t0, Y
241
242 bge t1, $fix_sign_in_ret1
243 cvttq/c $f0, $f0
244 _FTOIT $f0, Q, 8
245 .align 3
246 negq Q, Q
247 br $fix_sign_in_ret2
248
249 .align 4
250$fix_sign_out:
251 /* Now we get to undo what we did above. */
252 /* ??? Is this really faster than just increasing the size of
253 the stack frame and storing X and Y in memory? */
254 and t5, 4, AT
255 negq Y, t4
256 cmovne AT, t4, Y
257
258 negq X, t4
259 cmovlbs t5, t4, X
260 negq RV, t4
261 cmovlbs t5, t4, RV
262
263 br $fix_sign_out_ret
264
265 cfi_endproc
266 .size __remq, .-__remq
267
268 DO_DIVBYZERO
269

source code of glibc/sysdeps/alpha/remq.S